Question: Reduce to lowest terms: $ \dfrac{9}{4} \div - \dfrac{1}{9} = {?}$
Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $- \dfrac{1}{9}$ is $- \dfrac{9}{1}$ Therefore: $ \dfrac{9}{4} \div - \dfrac{1}{9} = \dfrac{9}{4} \times - \dfrac{9}{1} $ $ \phantom{ \dfrac{9}{4} \times - \dfrac{9}{1}} = \dfrac{9 \times -9}{4 \times 1} $ $ \phantom{ \dfrac{9}{4} \times - \dfrac{9}{1}} = \dfrac{-81}{4} $